Equilibrium Equivalence with J Candidates and N Voters

In this paper, we examine the incentives facing candidates in the spatial voting model. We assume that voters' types are independent, but allow for nonidentical distributions across voters. Examining candidate positional equilibria as a function of voter behavior, we find that what we term p-symmetric strict p-local equilibria when candidates maximize expected plurality are also strict p-local equilibris when candidates maximize probability of victory. This result holds for arbitrary numbers of candidates and voters. We also show that, for generic type distributions, interior p-asymmetric equilibria under maximization of expected vote share are not equilibria under maximization of probability of victory.